Solve

Original equation

Add 1 to each side to isolate the radical.

Square each side to eliminate the radical.

Find the squares.

Add 2 to each side.

Check

Answer: The solution checks. The solution is 38.

Replace y with 38.

Original equation

Simplify.

Answer: 67

Solve

Solve

Original equation

Square each side.

Find the squares.

Isolate the radical.

Divide each side by –4.

Answer: The solution does not check, so there is no real solution.

Check

Square each side.

Evaluate the squares.

Original equation

Evaluate the square roots.

Replace x with 16.

Simplify.

Solve .

Answer: no real solution

Solve

In order to remove the power, or cube root, you must

first isolate it and then raise each side of the equation to

the third power.

Original equation

Subtract 5 from each side.

Cube each side.

Evaluate the cubes.

Answer: The solution is –42.

Divide each side by 3. Check

Original equation

Add.

Replace y with –42.

Simplify.

The cube root of –125 is –5.

Subtract 1 from each side.

Answer: 13

Solve

Solve

Since the radicand of a square root must be greater than or equal to zero, first solve to identify the values of x for which the left side of the inequality is defined.

Now solve .

Original inequality

Isolate the radical.

Eliminate the radical.

Add 6 to each side.

Divide each side by 3.

Answer: The solution is

CheckTest some x values to confirm the solution. Let

Use three test values: one less than 2, one between 2 and 5, and one greater than 5.

Only the values in the intervalsatisfy the inequality.

Since is not a real number, the inequality is not satisfied.

Since the inequality is satisfied.

Sincethe inequality is not satisfied.

Answer:

Solve